Quantum theory of invariants applied to the the Caldirola-Kanai time-dependent forced harmonic oscillator
Keywords:
Physics. Quantum theory. Time-dependent quantum oscillatorAbstract
In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the Caldirola-Kanai time-dependent forced harmonic oscillator in terms of the solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the quantum fluctuations in coordinate and momentum as well as the uncertainty product. It is also shown that the quantum fluctuations and the width of the Gaussian packet do not depend on the external force.Downloads
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de Lima, A. L., & Pedrosa, I. A. (2011). Quantum theory of invariants applied to the the Caldirola-Kanai time-dependent forced harmonic oscillator. Scientia Plena, 4(10). Retrieved from https://scientiaplena.org.br/sp/article/view/617
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